i=j(interactions between two molec.),4Chapter 1.IntroductionorEtot(n1,n2,...,nN) =N

i

E0i+Uini+12Yin2i

+N

i=jninjJij2,(1.2)where the energy of a single atom was approximated by a second-order Taylor ex-pansion about the neutral atom.Jijis the Coulombic interaction between one elec-tron located at atomic positioniand another at the position of thejthatom,thusJij= e2/0dij.The coefﬁcientsUiandYiare the Mulliken electronegativity and thehardness of the isolated atom,respectively,and are deﬁned using the electron afﬁnityχiand the ionization potentialIiof the atom asUi= χi/2 +Ii/2andYi= Ii−χi.The task is then to minimizeEtot,subject to the constraint that the net charge of themolecule is zero.The charge transfer can then be estimated from the requirementthat,in thermal equilibrium,the electrochemical potential (∂Etot/∂ni),is constantthroughout the molecule.To apply this ECPE method in order to estimate the charge transfer and electricdipole at a MS interface,Tung regarded the entire MS region (the ’interface speciﬁcregion’) as a giant molecule.A few planes of atoms each fromthe semiconductor andmetal lattices are included in this molecule.A further assumption is that the chargetransfer only occurs between atoms directly involved in the interface bonds.By givingthe atoms bulk characteristics,the Mulliken electronegativity and the hardness canbe written as:UM= φM,YM= 0,US= χs+Eg/2andYS= Eg,whereφMis thework function of the metal andEgis the band gap of the semiconductor.Finally (aftersome calculations,see [10,11]),the SBH is:Φ0B= γb(φM−χs) +(1 −γb)Eg2,(1.3)wherein the ’interface parameter’ is:γb= 1 −e2dMSNb

int(Eg+κ).(1.4)dMSis the distance between the metal and semiconductor atoms at the interface,Nbthe uniformdensity of chemical bonds,

intthe permittivity of the interface region,andκthe sumof all the hopping interactions.Equation 1.3 predicts the same weak dependence of the SBH on the metal workfunction,as predicted by other ’gap state models’ (e.g.MIGS [12–14]).There are‡Walter Hermann Schottky lived from 1886 to 1976.¶Sir Neville Francis Mott lived from 1905 to 1996,and shared the 1977 nobel prize in physics withP.Anderson and J.van Vleck.5Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMhowever,quite some issues which remain unsettled about the application of the ECPEmethod at MS interfaces.But most important is the validity of the overall view onthe bonding-related charge transfer at the interface.1.2 Electrical behaviour of the Schottky BarrierTO UNDERSTANDthe electrical behaviour of a Schottky Barrier,ﬁgure 1.2 showsthe inﬂuence of an external applied bias on the SB.For a positive or forward bias(i.e.negative bias applied on the n-type semiconductor,compared to the metal),thereis a reduction in the barrier,as seen by the electrons coming fromthe semiconductorside.The barrier on the metal side remains the same,independent of the appliedbias,and this barrier is called the SBΦB.When an electron is transported acrossFigure 1.2:Schottky barrier under with external applied bias,(a) no bias,(b)forward bias,(c) reverse bias.a SB,the electric ﬁeld produced by this particular electron causes a lowering of thebarrier.This is called the image-force effect and the effect is shown in ﬁgure 1.3(a).Special about it,is that this lowering is absent if there is no electron in the conductionband near the top of the barrier.More explanation about this and other effects thatinﬂuence the electrical behaviour,can be found in e.g.the work of Rhoderick andWilliams [15].Figure 1.3(b) shows the various ways in which electrons can be transported acrossa MS junction (n-type semiconductor) under forward bias.The inverse processes oc-cur under reverse bias.The mechanisms are:6Chapter 1.IntroductionFigure 1.3:(a) Image-force lowering of the barrier.(b) Transport processesin a forward-biased Schottky barrier.(a) emission of electrons from the semiconductor over the top of the barrier into themetal;(b) quantum-mechanical tunnelling through the barrier;(c) recombination in the space-charge region;(d) recombination in the neutral region (’hole injection’).Process (a) is the most important in most of the Schottky diodes and the other pro-cesses are regarded as departures of this ideal behaviour.The thermionic emissiontheory of Bethe [16] describes the current transport asJ =IA= A∗T2e−ΦBkbT

eqVkbT−1

,(1.5)where a Richardson constant is deﬁned asA∗=4πm∗qk2bh3.(1.6)Ais the surface of the diode,kbis the Boltzmann constant,Tthe temperature,m∗the semiconductor effective electron mass,qthe magnitude of the electronic charge,andhPlanck’s constant.To account for the image-force effect on the current-voltage relationship,an ideal-ity factornis induced in the relationship.It is deﬁned as the inverse of the slope of theI-V curve,normalized by that expected of the perfect thermionic emission process,or:n =

1 −

∂ΦBq∂V

−1.(1.7)7Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMIn real devices,the applied bias across the interface can be diminished by voltagedrops across the Ohmic contact and the bulk semiconductor.If the effect of this seriesresistance is taken into consideration,an Ohmic drop ofIRSshould be subtractedfrom the applied bias to obtain the actual voltage drop across the MS interface.Oneﬁnally gets as useful relation:J =IA= A∗T2e−ΦBkbT

eq(V −IRS)nkbT−1

.(1.8)1.3 The inhomogeneous Schottky barrierASCHOTTKY BARRIERwhich has lateral variation in its BH,i.e.along the MS in-terface,is named ’inhomogeneous’.This means that along the MS interface,’patches’ exist,which have their own (higher or lower) SBH.This can be due to theinﬂuence of chemical bonds (see the BPT),but also due to the presence of charges,defects,interfacial layers,....One of the ﬁrst models that describes the current of aninhomogeneous SB is the ’parallel conduction model’ [5],where the total current isthe sumof the contributions from every individual area,meaningI(V ) = A∗T2

eqVkbT−1

iAie−ΦikbT,(1.9)whereAiandΦiare the area and the SBH of the i’th patch,respectively.The mainassumption behind the parallel conduction model is the independence of the differ-ent segments of an interface,of each other.However,there are some phenomenaobserved (e.g.greater-than-unity ideality factors,theT0anomaly,leakages,the de-pendence of the SBH on the measurement technique,...) that cannot be explainedusing this model,unless assumptions are made like e.g.a temperature dependenceof the SBH and ideality factor.However,the physical reason for the variation of theseparameters is unknown in these analysis.Furthermore,numerical simulations at MSinterfaces revealed that the parallel conduction model is in signiﬁcant error when theSBH varies spatially on a scale less than,or comparable to,the width of the spacecharge region [17].The"Pinch Off"(PO) theory [7] gives a coherent explanation of many of theseanomalies in the experimental results.The main difference to the previous theoriesis that the PO theory takes into account the interaction between neighbouring sec-tions of the same interface.For example,when a small patch with a low SBH issurrounded by high SBH patches,the interaction between them will cause the smallpatch to be ’pinched off’.This means that if an electron would come fromoutside thespace-charge region,it would have to overcome a higher potential barrier than theband-edge position at the MS interface,in order to reach the MS interface.Figure1.4 shows two illustrations of such a situation.One can see that the potential at thesaddle point (marked with an arrow) is higher than the potential at the interface.Using8Chapter 1.IntroductionFigure 1.4:Three-dimensional views of the potential distribution in front ofa low SBH patch in a high SBH background.The arrow marks the saddlepoint.this PO theory,Tung explained several experimental phenomena that had no (or onlyempirical) explanations.Tung assumes a Gaussian distribution of circular patches∗with an area density ofpatchesρpwith a constant barrier height:N(γ) =ρp√2πσ2e−γ2σ2.(1.10)Here,γ = 3(R2p∆p/4)1/3,with∆pthe patch parameter.∆pis the deviation of thelocal barrier height from the homogeneous valueΦB0,Rpthe radius of the circularpatch,andσthe standard deviation.The total current through such patchy diodesbecomes:Itotal= AA∗∗T2exp

−ΦB0kbT

exp

q (V −RSItotal)kbT

−1

(1.11)×

1 +8πρpσ2η1/39 (Vb0−V +RSItotal)1/3exp

q2σ2(Vb0−V +RSItotal)2/32k2bT2η2/3

,withη = s

0/qND,

sand

0the permittivity of the semiconductor and the vac-uum,respectively,NDthe dopant concentration,Rsthe series resistance of the semi-conductor bulk and the measurement setup,andVb0the band-bending of the uniformbarrier at zero bias.∗In Tung’s article,one can ﬁnd the calculations for the case of strip-patches,and/or for an isolatedpatch.9Bibliography[1] R.T.Tung.Mater.Sci.Eng.R-Rep.,35(1-3):1,2001.[2] W.Schottky.Z.Physik,113:367,1939.[3] N.F.Mott.Proc.Roy.Soc.(London),171:27,1939.[4] R.T.Tung.Phys.Rev.Lett.,52(6):461,1984.[5] I.Ohdomari and K.N.Tu.J.Appl.Phys.,51(7):3735,1980.[6] Y.P.Song,R.L.Vanmeirhaeghe,W.H.Laﬂere,and F.Cardon.Solid-StateElectron.,29(6):633,1986.[7] R.T.Tung.Phys.Rev.B,45(23):13509,1992.[8] W.J.Kaiser and L.D.Bell.Phys.Rev.Lett.,60(14):1406,1988.[9] H.Sirringhaus,T.Meyer,E.Y.Lee,and H.vonKanel.Phys.Rev.B,53(23):15944,1996.[10] R.T.Tung.Phys.Rev.Lett.,84(26):6078,2000.[11] R.T.Tung.Phys.Rev.B,6420(20),2001.[12] F.Flores and C.Tejedor.12(4):731,1979.[13] J.Tersoff.Phys.Rev.Lett.,52(6):465,1984.[14] J.Tersoff.Phys.Rev.B,32(10):6968,1985.[15] E.H.Rhoderick and R.H.Williams.Metal-Semiconductor Contacts.ClarendonPress,Oxford,second edition,1988.[16] H.A.Bethe.MIT Radiation Lab.Rep.,43:12,1942.[17] J.L.Freeouf,T.N.Jackson,S.E.Laux,and J.M.Woodall.Appl.Phys.Lett.,40(7):634,1982.Chapter2Conducting probeAtomic Force Microscope2.1 Atomic Force MicroscopyBINNIG ANDQUATE[1] announced the birth of the Atomic Force Microscope (AFM)as a combination of the principles of the scanning tunnelling microscope (STM)and the stylus proﬁlometer (SP).Like STM,AFM supplies a three dimensional imageof a surface,with a high spatial resolution.An AFM operates by measuring attractive or repulsive forces between a tip andthe sample.For this,a small tip at the end of a (very ﬂexible) cantilever (see ﬁg-ure 2.1) is brought near the surface.Due to the forces between the atoms of thetip and the atoms of the surface (repulsive or attractive,depending on the distancebetween the atoms involved),the cantilever will deform elastically.By measuring thisdeformation,a topographical image of the surface can be made.The force is de-ﬁned by Hooke’s lawF = k × δzwithkthe force constant of the cantilever andδzthe movement/deformation of the cantilever.There are two commonly used scan-modes,namely the contact mode and the non-contact mode (the intermittent modealso exists,but is not discussed).In the ﬁrst mode,the tip is brought in contact withthe surface (which makes the force repulsive).A feedback mechanism moves thesample (or tip) up or down,to compensate the deformation of the cantilever.In thenon-contact mode,the distance between tip and sample is typical10nm− 100nm,and the force is attractive.The cantilever oscillates at a certain frequency,and whenthe distance between tip and surface changes,the frequency will alter.Keeping theoscillating frequency constant by moving tip or sample,one gets the topographicalinformation through the feedback mechanism.Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMFigure 2.1:Scanning Electron Microscope (SEM) images of (a) an AFMcantilever,(b) and (c) AFM tips.There are lots of options for the detection of the cantilever-deﬂection:STM(!) [1],capacitance measurements,optical interferometry [2] and laser beam deﬂection [3].The latter is the technique used in our system,and will be brieﬂy discussed.For moreinformation on the use of AFM,we refer to [4].Figure 2.2:AFM feedback mechanism monitoring the cantilever deﬂectionof a laser beam and adjusting the height of the sample.During the operation of the AFM,a laser beam is reﬂected on the back of thecantilever and detected by a position sensitive photodetector (PSD) (see ﬁgure 2.2).If the height of the cantilever would change,the reﬂected laser beamwill move on thePSD.The feedback mechanismnowcontrols the Z-piezo-element to move the sample14Chapter 2.Conducting probe Atomic Force Microscopy (C-AFM)up or down,until the reﬂected beam is back at its original position.Controlling andregistering the z-position of the sample,while it is scanned in x- and y-direction,willgive a topographic image of the scanned surface.2.2 The conducting probe AFMEVERsince Binnig and Quate published their invention of the AFM,its usage inresearch has increased year after year.In microelectronics,the technique hascertainly proved its worth,as it enables to envisualize submicron- and nano-sizedstructures.Due to the miniaturization in microelectronics,it also became harder totest the structures electrically.Therefore,mid the 1990s [5],the AFM was equippedwith a conducting probe and researchers tried to combine the excellent topographicalproperties of the AFM,with (known) electrical characterization techniques.The C-AFM technique has been used for a wide variety of applications:to mea-sure the resistances of individual molecules and nanoparticles [6],to examine dopantproﬁles [7],to measure oxide thicknesses in semiconductor devices [8],to imagecontact resistances across the surfaces of metals [9],and to measure current-voltagedependencies on individual organic semiconductor grains [10].The work of Freitaget al.[11] is relevant in the scope of our work.They used a C-AFM to measure localelectronic properties of single-wall nanotube circuits,and thus proved the applicabilityof this technique in the ﬁeld of the miniaturization of microelectronics.It is however,the work of Hasegawa et al.[12–15] which has the biggest link to previous SB re-search.They formed nanometer-sized MS interfaces on GaAs and InP by an in situelectrochemical process,and used C-AFM to measure the I-V characteristics.Thecharacteristics of the nano-sized contacts showed non-linearlogI − Vcurves withlarge,voltage-dependent ideality factors,which is one of the typical phenomena forinhomogeneous SBHs.When using the C-AFM for electrical characterization,the contact between theAFM-tip and the sample is crucial.Bietsch et al.[16] give an overview of the basicmechanical requirements for the C-AFM tips:•mechanically robust:the tip must survive the forces applied when scanning andthe additional forces applied to form an electrical contact;•chemically inert:no passivation by oxidation or electrochemically induced re-actions should occur that could interfere with the conductivity of the tip;•sharp:for a good resolution of the scan images.Off course,the electrical characteristics of the tip are very important.Schneeganset al.[17] characterized the nano-contact between an n-doped silicon tip and a cop-per sample.They found that this tip-sample system can be considered as an ideal15Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMSchottky diode with a certain resistance in series.However,to characterize the SBat the MS interface,and not at the tip-sample interface,metal-coated or (very) highlydoped semiconductor tips are preferred.Bietsch et al.[16] suggest platinum-coatedtips as having the suitable mechanical stability and a low-ohmic behaviour on variousmetals.Trenkler et al.[18] address the issue that metal-coated tips are frequentlyaffected by wear,and therefore propose the tips with a conductive (i.e.highly-doped)diamond coating as extremely useful.A downside on this last kind of tips is the pos-sible tip-to-tip variation in doping.The work of Thomson et al.[19] agrees with theconclusion of Trenkler,for the wearing of the metal-coated tips.However,they stressthat with the metal-coated tips,much lower contact resistances can be obtained.Asa solution to the wear of the tip,they suggest to use the intermittent mode to scan thesurface,instead of the contact mode.2.3 Our C-AFM systemTHEAFMSYSTEMavailable is a Topometrix TMX2010,for which the C-AFM op-tion is homebuilt (see ﬁgure 2.3).It consists of a computer-controlled (througha DAC-interface card) power supply with a range from−10Vto+10V.For practicaluse (as the measurement range is mostly between−1Vand+1V),a1/10-voltagedivider is included in the system to get a better bias-resolution.The bias is appliedbetween the conducting tip and the sample.The back of the sample (with Ohmiccontact) is connected with a Keithley 616 electrometer,by the sample-holder.Theelectrometers current-sensitivity ranges from10Ato10−14A,with a manual selectionof the sensitivity.The electrometer acts as aI −Vconverter between sample andcomputer,which registers the converted voltages.Before discussing the tips and cantilevers that were used,we elaborate on theprocedure to measure an I/V-characteristic with this homebuilt C-AFM.Firstly,an im-age can be made using the AFM in its normal operation mode.Once this overviewimage is made,one zooms in to make sure that the tip is above the contact.If the con-tact is still easily visualized on the CRT-screen of the apparatus (which uses lensesto get a good picture),it is not necessary to perform this topography-scan and thetip can be manually positioned above the contact.Then,the laser is switched off toavoid a photocurrent that would originate from the scattering of the laser light ontothe sample.Doing this,the feedback mechanism of the AFM is interrupted,so we donot know what amount of force is applied to the tip.We manually lower the tip ontothe contact and apply as much force as needed to establish an electrical contact.Aphotocurrent can be observed,due to the light of the internal microscope of the AFM.Fromliterature [19] it is known that the force needed for electrical measurements is ofthe order ofµN,while for scanning purposes it is of the order of nN.Lantz et al.[20]also predict that if C-AFM is undertaken in air (they work in UHV),very large forces,of the order ofµN,will be required to establish a stable electrical junction,due to16Chapter 2.Conducting probe Atomic Force Microscopy (C-AFM)Figure 2.3:Scheme of the homebuilt C-AFMsystem.contamination of the tip and sample surface.Once this contact is established,we switch off the light and apply a bias to checkif we still have electrical contact.If the current ﬂuctuates,we can increase the pres-sure of the tip on the contact,by increasing the bias on the z-piezo,thus pushingthe sample towards the tip.If we cannot establish a good,stable current,we repeatthe process or replace the tip (wear of the coating).It is easier to establish a stablecontact with a rather stiff cantilever (with a force constant of about0.6to1.8N/m)than with a more ﬂexible cantilever (order of50mN/m).If a stable electrical contact isestablished,the bias-sweep and the current registration are started.Two kinds of C-AFM tips were used in this research:Ultrasharp contact siliconcantilevers (and tips) with either a25nmPt-coating,or a20nmCr/20nmAu-coatingon both sides (i.e.the tip side and the reﬂection side).The cantilevers are rectangular(see ﬁgure 2.4),and have different force constants.The tip has a height of≈ 20µm,a tip cone angle of less than20◦and the radius of the curvature is less than35nmor50nmfor thePt- orCr/Au-coated tips,respectively.As shown in appendix A,there was no difference noticed between the two coatings,or the different force con-stants.We prefer the usage of Pt-coated tips,due to the longer lifetime of the coating.To determine the series resistance of our measuring-unit (i.e.coming mainly fromthe tip-cantilever unit),I/Vmeasurements were done on a gold layer with aPt-coated tip and are shown in ﬁgure 2.5(a).A good Ohmic behaviour is observed,and17Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMFigure 2.4:SEM image of the cantilevers (and tips) used in the C-AFM re-search.fromthe measurements (and Ohm’s law),an average series resistance of407Ωis de-termined.There is a very good agreement between our value,and the one obtainedby Thomson and Moreland [19].For n-dopedSicantilevers coated with45nm Pt,they found a series resistance of350Ω,measured on a50nmgold layer.Figure 2.5(b) shows a forward and reverse I/V-curve of a Au/n-GaAs Schottkycontact,measured using the C-AFM.We can clearly see the rectifying behavior ofthe contact.Due to the time consumption of measuring the reverse part,we haverestricted our other measurements to the forward part of the I/V-curve.We will beusing theseI/Vcharacteristics to determine BHs and ideality factors for the Schottkycontacts.Therefore,we determined the error on both parameters that originates fromthe measuring setup (see appendix A for more details):error(φB) = 0.003eV and error(n) = 0.009.18Chapter 2.Conducting probe Atomic Force Microscopy (C-AFM)Figure 2.5:(a) I/V-measurements of a gold layer with the Pt-coated tip showsa good Ohmic behaviour.(b) I/V-measurement on a Au/n-GaAs Schottkycontact with a Pt-coated tip,shows a good rectifying behaviour.19Bibliography[1] G.Binnig,C.F.Quate,and C.Gerber.Phys.Rev.Lett.,56(9):930,1986.[2] D.Rugar,H.J.Mamin,and P.Guethner.Appl.Phys.Lett.,55(25):2588,1989.[3] G.Meyer and N.M.Amer.Appl.Phys.Lett.,53(12):1045,1988.[4] Veeco Instruments Inc.A practical guide to Scanning Probe Microscopy.2005.[5] S.Morita,Y.Sugawara,and Y.Fukano.Jpn.J.Appl.Phys.Part 1 - Regul.Pap.Short Notes Rev.Pap.,32(6B):2983,1993.[6] B.Alperson,S.Cohen,I.Rubinstein,and G.Hodes.Phys.Rev.B,52(24):17017,1995.[7] P.Dewolf,J.Snauwaert,L.Hellemans,T.Clarysse,W.Vandervorst,M.Dolies-laeger,and D.Quaeyhaegens.J.Vac.Sci.Technol.A,13(3):1699,1995.[8] A.Olbrich,B.Ebersberger,and C.Boit.Appl.Phys.Lett.,73(21):3114,1998.[9] F.Houze,R.Meyer,O.Schneegans,and L.Boyer.Appl.Phys.Lett.,70(26):3619,1997.[10] T.W.Kelley and C.D.Frisbie.J.Vac.Sci.Technol.B,18(2):632,2000.[11] M.Freitag,M.Radosavljevic,W.Clauss,and A.T.Johnson.Phys.Rev.B,62(4):R2307,2000.[12] H.Hasegawa,T.Sato,and C.Kaneshiro.J.Vac.Sci.Technol.B,17(4):1856,1999.[13] T.Sato,S.Kasai,H.Okada,and F.Hasegawa.Jpn.J.Appl.Phys.Part 1 - Regul.Pap.Short Notes Rev.Pap.,39(7B):4609,2000.[14] T.Sato,S.Kasai,and H.Hasegawa.Jpn.J.Appl.Phys.Part 1 - Regul.Pap.Short Notes Rev.Pap.,40(3B):2021,2001.[15] T.Sato,S.Kasai,and H.Hasegawa.Appl.Surf.Sci.,175:181,2001.Chapter 2.Conducting probe Atomic Force Microscopy (C-AFM)[16] A.Bietsch,M.A.Schneider,M.E.Welland,and B.Michel.J.Vac.Sci.Technol.B,18(3):1160,2000.[17] O.Schneegans,L.Boyer,F.Houze,R.Meyer,and P.Chretien.J.Vac.Sci.Technol.B,20(5):1929,2002.[18] T.Trenkler,T.Hantschel,R.Stephenson,P.De Wolf,W.Vandervorst,L.Helle-mans,A.Malave,D.Buchel,E.Oesterschulze,W.Kulisch,P.Niedermann,T.Sulzbach,and O.Ohlsson.J.Vac.Sci.Technol.B,18(1):418,2000.[19] R.E.Thomson and J.Moreland.J.Vac.Sci.Technol.B,13(3):1123,1995.[20] M.A.Lantz,S.J.O’Shea,and M.E.Welland.Rev.Sci.Instrum.,69(4):1757,1998.22Chapter3Experimental DetailsALLsamples were prepared using0.35mmthick,n-doped GaAs(100) wafers (Sidoped),obtained fromWafer Technology Ltd.The average carrier concentrationisND≈ 4x1016cm−3and the resistivity varies from0.076to0.078 Ωcm.The wafershave a polished front side.Samples of5by5 mm2were cut fromthe wafers.The samples were degreased subsequently in boiling trichloroethyleneC2HCl3,acetoneCH3COCH3and methanolCH4O.Afterwards,they were chemically etchedin a 3:1:1 (volume ratio) mixture of sulfuric acidH2SO4(95%),hydrogenperoxideH2O2(27%)and deionised (DI) waterH2O,at80◦C.Immediately afterwards,theywere dipped for5sin a1:1mixture of chloric acidHCl(37%)and DI waterH2Oatroom temperature,to remove the native oxide.Finally the samples were rinsed in DIwater and dried withN2.Ohmic contacts were made at the back of the samples by thermal evaporation ofIn in a vacuumof about10−5mbar,with the substrate held at roomtemperature.Thiswas followed by annealing the samples at300◦Cfor 10 min in an inert atmosphere(N2).For the fabrication of the Schottky contacts,Electron Beam Lithography (EBL)was used‡.This technique is comparable to standard lithography techniques,withthe difference being the use of electrons to pattern the samples,instead of UV-light.Due to the shorter wave length of electrons,smaller structures can be patterned.Forthis,a JEOL scanning electron microscope (SEM),type JSM T-330,is used with ahomebuilt lithography software.After cleaning the samples,a double layer of (posi-tive) photoresist is spin-coated on the surface.The ﬁrst photoresist layer is a200nmthick poly(methyl methacrylate)/methacrylic acid copolymer (PMMA/MAA) layer,andis baked for15minutes at165◦C.The top layer is180nmof PMMA,baked for30minutes at165◦C.Using EBL,squares with different sizes are patterned in the photoresist.ThePart I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMFigure 3.1:SEMimage of (a) the lift-off process (the marker indicates50µm)and (b) Au/n-GaAs contacts that were made by EBL and measured with C-AFM (the marker indicates100µm).lengths of the sides are:150µm,100µm,50µm,20µm,10µm,9µm,8µm,7µm,and6µm.There were also squares with sides of2µm,1µmand< 1µm.After e-beampatterning,the structures were developed in a MIBK (methyl-isobutyl-ketone):IPA (isopropanol) solution with 1:2 concentration at room temperature.After-wards,they were rinsed in pure IPA and dried withN2.Prior to the gold evaporation,some of the patterned samples were dipped for 5 s inHCl:H2Oand rinsed in DI water (see chapter 4 for further details and results).TheSchottky contacts were made by evaporating30nmgold onto the sample at a rateof0.15nm/sin a vacuum better than4 ×10−6mbar,with a substrate temperatureof100◦C.Finally,a lift-off process was performed on the samples using acetone,slightly heated to maximum30◦C.Figure 3.1 shows SEM images of an incompletelift-off process (a) and of some Au/n-GaAs contacts that were typically made (b).‡See appendix B for an illustration of the EBL process24Chapter4The SBH inhomogeneities inidentically prepared Au/n-GaAsSchottky contactsEVERsince Tung published his PO theory,there has been research to ﬁnd outmore about the inhomogeneities and their inﬂuence on the Schottky contact.Furthermore,due to the downscaling in microelectronics,the inﬂuence of these inho-mogeneities might become more pronounced,so a more complete characterisationof the SBHand its inhomogeneities is of interest.Then again,miniaturization can alsohelp in the search for experimental evidence for the newly published BPT (see chapter1):by downscaling the Schottky contacts,one might be able to distinguish more theinﬂuence of certain parameters and their (local or general) effect on the SBH.The de-velopment of the C-AFM technique supplied a promising characterisation techniqueto investigate the correlation between the inhomogeneities and the downscaling.In this chapter,we ﬁrst discuss the technical issues for measuring submicronSchottky contacts,followed by a more elaborate investigation of the ’micron’ contacts(6to150µm).Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFM4.1 The submicron Schottky contactsTHEEBL technique enables us to create diodes with small sizes,but it also al-lows us to create them with a certain shape and position relative to each other.Figure 4.1:SEMimages of some small square-shaped contacts made usingEBL.The length-scale (bottom right) is1µmfor both images.Figures 4.1 and 4.2 show some examples of the small-sized contacts that were fab-ricated using the EBL-technique.The (a)-parts of the ﬁgures illustrate the possibilityfor contact-placement,while the (b)-parts of the ﬁgures show a zoomed image of thecontact to give a better idea of the size of the contact.Figure 4.3 shows AFMimagesof similar contacts.The C-AFM setup should enable us to measure these small-sized contacts.Asexplained in section 2.3 (page 16),a topographic image (like ﬁgure 4.3(b)) is taken,and then the scanning range is zoomed in on the contact,to move the tip on top of thecontact.Normally,one should be able to measure I/V-characteristics on these smallcontacts.However,we did not succeed in this.Due to the necessity to block out any light,the feedback-mechanism (with laser)used for topographical scanning,needs to be switched off.This causes the tip tomove upwards to its default position (above the surface).Theoretically,when the tipis lowered again,it should be at the same position as when the feedback-loop wascut.However,it seems that most of the time,this is not the case.Furthermore,whena ﬁrst electrical contact was established between tip and small-scale contact,it waseither not stable (in current at a ﬁxed bias) or it disappeared after a short time.26Chapter 4.The SBH inhomogeneities in identically prepared Au/n-GaAs Schottky contactsFigure 4.2:SEM images of some small circular contacts made using EBL.The length-scale (bottom right) is either (a)5µmor (b)1µm.The most probable cause for this failure,are the piezo elements which are usedto position the sample.A small change in bias over the piezo element,can causea small change in position of the sample.With the feedback-mechanism on,thischange in position would be corrected for.We also believe that temperature changesoriginating from the current density or the environment,cause a small displacementof the sample.A different sample stage is the ﬁrst step in solving the problem.Afeedback-mechanism that doesn’t use light (or at least not in the neighbourhood ofthe sample) is a necessity to keep the sample at its correct position.Figure 4.3:AFM images of some small circular contacts made using EBL.27Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFM4.2 The micron Schottky contactsFORthe Au/n-GaAs Schottky contacts with dimensions ranging between6µmand150µm,we observed a difference in electrical characteristics,depending on acertain fabrication process.Group A consists of 108 diodes,made using the standardEBL-technique,as described in chapter 3.Group B comprises 260 diodes who gotan extraHCl-dip∗,right before they were mounted in the evaporation machine for theAu deposition.Figure 4.4:Histograms of the SBH’sφeffand ideality factorsnefffor thediodes of group A and group B,respectively,determined using the TEmodel.The inset in (d) shows the histogram on the same x-scale as in(b).Gaussian curves were ﬁtted to the results.∗The term"HCl-dip"is used here to describe both the 5s dip inHCl:H2Oand the rinsing in DIH2O.28Chapter 4.The SBH inhomogeneities in identically prepared Au/n-GaAs Schottky contactsFor each diode,the SBH and ideality factor were calculated using the TE model(see equation 1.8) and we will refer to these asφeffandneff,respectively.All diodeswithin each group were identically prepared,but they exhibit a difference in SBHand ideality factor.The diodes were by no means ideal;their ideality factors arelarger than the ideality factor determined by the image-force effect (see section 1.2)which is close to1.01.Figure 4.4 shows a summary of the results,by means of ahistogram for each group and each parameter.Concerning the ideality factors,oneclearly observes that the group B -diodes are ’more ideal’ (i.e.ideality factors closer to1).The inset of ﬁgure 4.4(d) shows the histogramof the ideality factors of group B onthe same x-scale as for the histogramfor group A.This clearly shows that the spreadon the ideality factors is much smaller for group B.The spread on the SBH’s shows asimilar behaviour,and one observes that the SBHs of group A are (generally) largerthan for group B.Gaussian curves were ﬁtted to the histograms,which supplied uswith averages for the parameters:group A group B< neff>1.202 1.057< φeff>(eV) 0.920±0.028 0.819±0.010From the histograms and the gaussian curves,one could conclude that the ide-ality factor and the SBH are higher for the diodes of group A,compared to the onesfor group B.However,the histograms disregard the pronounced correlation betweenthe effective barrier heights and the ideality factors [1–4].They can illustrate a certaintrend in the results,but other parameters should be used to make a good comparisonbetween the two groups.When lateral inhomogeneities occur,the saddle-point potentials in front of small-size patches are lower than the SBH of the surrounding regions.Tung [5] derived ananalytical expression for theI/Vcharacteristics of laterally inhomogeneous Schottkycontacts,as explained in section 1.3.The equation derived by Tung supplies us with a method of determining a homo-geneous barrier height,which we note asΦB0.Using equation (1.11) withΦB0,σ,ρpas ﬁtting parameters,all the experimentalI/Vcharacteristics were ﬁtted.Figure 4.5shows two experimental curves,each from a different diode,with their ﬁtted curves.One can see that the ﬁtted curves closely followthe experimental data.Fromall thesePO parameters,obtained by ﬁtting the curves,we derived the average values:group A group B< ΦB0>(eV) 1.021±0.037 0.848±0.016< σ >(V1/3cm2/3) 9.961×10−56.226×10−5< ρp>(cm−2) 3.790×1075.116×101029Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMFigure 4.5:I/V characteristics of two Au/n-GaAs Schottky diodes.The fulllines are ﬁts of Tung’s equation for patchy diodes.Schmittsdorf et al.[1,3] applied Tung’s theory to experimental data ofAg-,Pb-andSn/Si(111)diodes,and found that the linear extrapolation of the experimen-tally observedφeffvsneffcurves tonif(the ideality factor of the ideal diode,withimage-force included) gives the lateral homogeneous barrier heightΦhomlat.For com-pleteness,we deﬁnenifas [6]nif=

1 −14

q3ND8π2(s

0)3

1/4

ΦB0−V −ξ −kBTq

−3/4

−1.(4.1)They used sets ofφeff(neff)with ideality factors ofn < 1.4to make their linearﬁtting.To get an idea of the upper limit for the ideality factor for our contacts (since weare using a different substrate),we did a similar simulation as Schmittsdorf et al..Weused the average values< ΦB0>and< σ >(obtained previously for each system),and varied the patch densityρpstepwise from zero to1.0 × 109cm−2.Subsititutingthese parameters in equation (1.11),an I/V -curve is calculated for each value ofρp.Using the TE formula (equation (1.8)),values forφeffandneffare calculated.Fig-ure 4.6 shows the resultingφeff(neff)-plot for both groups.Linear regions can beassumed forn ≤ 1.18andn ≤ 1.17,for group A and group B respectively.30Chapter 4.The SBH inhomogeneities in identically prepared Au/n-GaAs Schottky contactsFigure 4.6:The full lines are numerical simulations using the average POparameters,and varying the patch density.The dashed line shows thelinear relation forφeff(neff)-values up ton ≤ 1.18andn ≤ 1.17for groupA and group B,respectively.Figure 4.7:Linear ﬁt of the experimentalφeff(neff)data points.The linearextrapolation tonif= 1.01gives a lateral homogeneous barrier heightΦhomlat(A) = 0.959 eVfor group A,andΦhomlat(B) = 0.835 eVfor group B.31Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMKnowing the upper limit for the linear ﬁtting,we can determine the lateral homoge-neous barrier heightΦhomlat,using the method of Schmittsdorf.Figure 4.7 shows theselinear extrapolations tonif,yielding:group A group BΦhomlat(eV)0.959 ±0.034 0.835 ±0.010Before discussing the results,we take a closer look at the pinch-off theory for amore physical picture of the patches.We can write the local lowering of the barrierheight at the saddle point in front of a circular patch of radiusRpas [5]δΦsadp= ΦB0−ΦsadB= 3

12∆pqVb0R2pW2

1/3qVb0,(4.2)whereW = [2s

0(Vb0−ξ)/qND]1/2is the depletion layer width,and∆pthe patchparameter (see equation (1.10) on page 9 for more explanation).Furthermore,thestandard deviationσmay be interpreted as an average patch-parameterσ =< γ >= 3

(∆pR2p/4)1/3

.(4.3)When we combine equation (4.2) and (4.3) with the averages obtained here,wecan make an estimation of the BH lowering by< δΦsadp>=< ΦB0−ΦsadB>= σ

2qVb0W2

1/3qVb0.(4.4)With these formulae,we calculate the following properties of the patches,for bothgroups:group A group B< δΦsadp>(eV) 0.173 0.102diameter2Rp(nm) 18 12%of W 10 732Chapter 4.The SBH inhomogeneities in identically prepared Au/n-GaAs Schottky contactsSummary:Table 4.1:Summary of the results for the two groups of Au/n-GaAs Schottkycontacts.The last column indicates the method used (TE:ThermionicEmission model,PO:Pinch-off model,S:Schmittsdorf method).Group A Group B< φeff>(eV)0.920 ±0.028 0.819 ±0.010TE< neff>1.202 1.057TE< ΦB0>(eV)1.021 ±0.037 0.848 ±0.016PO< σ >(V1/3cm2/3)9.961 ×10−56.226 ×10−5PO< ρp>(cm−2)3.790×1075.116×1010PO< δΦsadp>(eV)0.173 0.102POdiameter2Rp(nm)18 12POΦhomlat(eV)0.959 ±0.034 0.835 ±0.010STable 4.1 gives an overview of the parameters that were discussed.The val-ues for the homogeneous SBH determined using different techniques (PO-ﬁtting andSchmittsdorf-method),agree within the range of the experimental error.One can seefrom ﬁgure 4.7 that the linear ﬁt to theφeff(neff)data is better for group B than forgroup A.This results,for group A,in a bigger difference between the PO homoge-neous SBH and the lateral homogeneous SBH,although they are comprised withinthe error ranges.However,we may conclude that both methods are reliable forobtaining the value of the homogeneous SBH.Care should be taken when Schottkycontacts with large ideality factors are researched,and for these the PO method isprobably the most accurate to obtain the homogeneous SBH.Furthermore,from table 4.1 one can see a clear difference between the twogroups of diodes;the (homogeneous) SBH of group A diodes is always higher thanthe one for group B diodes.The difference between the diodes of the two groups,is aHCl-dip before gold deposition.AHCl-treatment is known in the GaAs-fabricationprocess to remove oxide layers.The oxygen contamination,which would still bepresent in group A diodes,can originate from the EBL-fabrication process.Duringthe fabrication,PMMA-resist layers are used,and also chemical solvents containingmuch oxygen,like IPA and MIBK (see chapter 3).Barbe et al.[7] reported the growthof thin oxide layers on GaAs in methanol.We believe a similar process occurs here,only in a more limited amount (i.e.a very thin oxide layer).33Part I.Electrical characterisation of Au/n-GaAs Schottky contacts using C-AFMBiber et al.[8] studied the effect of an anodic oxide growth on Au/n-GaAs Schottkycontacts.They found an increase by at least110 meVdue to the oxide.This iscomparable to the difference we observe between the diodes of the two groups.Fur-thermore,Forment et al.[9] observed a higher SBH for electrochemically-depositedAu/n-GaAs diodes than for vacuum-deposited ones.This difference is explained bythe presence of a dipole layer containing oxygen at the MS interface of the electro-chemical contacts.Because of the large electronegativity value of O,as compared toAu,it can be assumed that aAuδ+−Oδ−dipole is formed.The voltage drop acrossthis interfacial dipole then leads to an increase if the SBH.Our results conﬁrm these previously obtained results,and show the possibility tomodify the SBHfor vacuum-deposited samples using organic solvents.Even more,asa consequence of the POmodel,where only patches with a lower SBHare considered(see [5]),we ﬁnd the ’high SBH’ as the homogeneous SBH for the group A diodes.From the characterisation of the patches we found a BH-lowering of≈ 0.173 eV,which is comparable to the value found by Biber et al..So one could visualize thegroup A diodes as having a SBH dominated by theAuδ+− Oδ−dipole,with thepatches being places where the ’normal’ SBH (i.e.the SBH for group B diodes) ispresent.The experimental conﬁrmation of this ’dipole-model’ is very important regard-ing the acceptance of the BPT-theory [10],which states that the SBH is locally deter-mined by the bonding of the atoms forming the interface.34Bibliography[1] R.F.Schmitsdorf,T.U.Kampen,and W.Monch.J.Vac.Sci.Technol.B,15(4):1221,1997.[2] W.Monch.J.Vac.Sci.Technol.B,17(4):1867,1999.[3] R.F.Schmitsdorf and W.Monch.Eur.Phys.J.B,7(3):457,1999.[4] R.T.Tung.Mater.Sci.Eng.R-Rep.,35(1-3):1,2001.[5] R.T.Tung.Phys.Rev.B,45(23):13509,1992.[6] E.H.Rhoderick and R.H.Williams.Metal-Semiconductor Contacts.ClarendonPress,Oxford,second edition,1988.[7] H.Barbe,R.L.Van Meirhaeghe,and F.Cardon.Semicond.Sci.Technol.,3(9):853,1988.[8] M.Biber,M.Cakar,and A.Turut.J.Mater.Sci.-Mater.Electron.,12(10):575,2001.[9] S.Forment,R.L.Van Meirhaeghe,A.De Vrieze,K.Strubbe,and W.P.Gomes.Semicond.Sci.Technol.,16(12):975,2001.[10] R.T.Tung.Phys.Rev.Lett.,84(26):6078,2000.Part IITHIN FILM SOLID-STATE REACTIONSFORMINGCARBIDESChapter5General properties of carbides5.1 IntroductionWHENlooking to foreign atoms of all kinds in metal lattices,one will presumablystumble upon the term of Interstitial Alloy.This term implies the existenceof a pure metal lattice acting as a host to foreign atoms (of smaller size) which ﬁllthe room between the metal atoms (i.e.the interstices).However,this is only thecase for the primary solid solutions (and deﬁnes this group of interstitial alloys),butstill the term interstitial alloy is used in a more broadened sense.The most importantinterstitial alloys are the interstitial compounds,where the non-metal atom forms anintegral part of the compound.Without it,the metal lattice would differ entirely.Theinterstitial compounds have proven their worth and many examples of such materi-als will feel familiar:e.g.certain silicides,hydrides (like in nickel-metalhydride (NiMH)batteries),and off course the carbides.When reading the description of an interstitial alloy,steel was probably the ﬁrstmaterial that popped to mind.The most elementary steel is a solid solution of iron(Fe) and carbon.The ﬁrst indication towards the fabrication of steel (and not iron)tools,can be found in China around 500 BC.Around 250 BC,quality steel was madein India and spread around the world.Nowadays,China is by far the top steel produc-ing country.Of course,the steel produced nowadays has gone through a long periodof modiﬁcation,and it’s no longer only carbon which is dissolved in the iron.Otheratoms as chromium (Cr) and manganese (Mn) are added to improve certain prop-erties,but also amounts of iron carbide (Fe3C) are introduced into the steel.Steelhas become a complicated subject,being a mixture of all these elements,and it is aresearch topic in its own right.Part II.Thin ﬁlmsolid-state reactions forming CarbidesCARBIDESare interstitial compounds,where the non-metal atomis carbon.In thiswork,when we talk about carbides,we imply the transition metal carbides,where themetal is one of the transition metals.They have extremely high melting points,whichprocured themalso with the name of refractory carbides.Besides being stable at hightemperatures,they are extremely hard,and their hardness is retained to very hightemperatures,which are typical ceramic properties.Therefore,carbides have foundmany applications in the industry of cutting tools and wear-resistant parts.Tungstencarbide (WC) and titanium carbide (TiC) are the main players in this ﬁeld,and theycan be found on the tips of the so-called ’diamond-coated’ tools,and as scratch-resistant coatings in jewellery as wedding rings and watches.Carbides can also befound in more technologically advanced applications.WCis an efﬁcient neutronreﬂector and can be used in the ﬁeld of nuclear reactions (e.g.in nuclear weapons),niobium carbideNbCand zirconium carbideZrCare used as refractory coatings innuclear reactors.A (more peace-friendly) high-tech application is the use of carbidesas heat shields for the atmospheric re-entry of space shuttles and similar vehicles.In addition to their ceramic properties of high hardness and stability at high tem-peratures,carbides are also examined for their catalytic properties in a number ofreactions.Noble metals have been the commonly used catalysts for many years,butcarbides offer the potential to replace the expensive rare noble metal catalysts (Pt,Pd,Ru,Rh).A few ’hot’ catalytic processes being researched are the elimination (hy-drogenation) of the toxic carbon monoxideCO(CO+3H2−→CH4+H2O) [1],andthe decomposition of nitrogen monoxideNO(known from the pollutingNOxcom-pounds produced by cars etc.) toN2andO2gas,without forming other pollutants [2].Because of the lower production cost of the carbides,the carbides do not even haveto be more active in catalyzing given reactions,compared with the noble metals.The properties of some carbides will be summarized and discussed in section 5.2.Looking at the applications of the carbides mentioned above,one can easily seethat most of the research interest has gone to the mechanical properties of the car-bides.Nevertheless,more and more research concentrates on the electrical proper-ties of carbides,because there are now requirements for electrical materials that arehard,or that can sustain harsh environments.The conductivity of carbides is via elec-trons,not ions,but they have covalent,ionic and metal bonding,and therefore theyare often named metallic ceramics.It is within this area that our research ﬁnds itsplace.Some examples of this technologically advanced research on carbides are theuse of carbides to contact advanced semiconductors containing carbon like siliconcarbideSiC[3],diamond [4],and even carbon nanotubes (CNTs) [5].40Chapter 5.General properties of carbidesRegarding the formation of carbide materials,one can roughly distinguish threeforms of material appearance:powders,single crystals and thin ﬁlms [6].Each hasits typical and most popular techniques for preparing the carbides.Growing carbidesingle crystals is done using specialized techniques (which we won’t be discussinghere) as the Verneuil technique,the Czochralski technique,and other.The mostcommon powder-metallurgy technique is the direct reaction of metal or metal hydridepowders with carbon.These and other reactions used are summarized in Table 5.1.Table 5.1:Preparation techniques for carbide powders.Methode ReactionDirect reaction of metal with carbonM +C −→MCDirect reaction of metal hydridewith carbonMH +C −→MC +H2Reaction of the metal oxide andexcess carbon in inert or reducingatmosphereMxOy+C −→MC +COReaction of the metal with acarburizing gasM +CxH2x+y−→MC +H2M +CO −→MC +O2Reaction of the metal halide orcarbonyl vapour with hydrogenMCln+CxH2x+y−→MC +HCl +(CqHr)M(CO)n+H2−→MC +(CO,CO2,H2,H2O)These powder-based methods require several hours of annealing at temperaturesover2000◦C,with a great inﬂuence of these parameters on the homogeneity and ﬁnalcomposition of the carbide.An advantage to the high temperatures used,is that thecarbide can be puriﬁed fromoxygen contamination under certain conditions,such asa good vacuum.Thin ﬁlms of carbides are probably the most useful for applications,especially ifone considers the electronics industry.Some possible applications include:inter-connects that do not suffer fromelectromigration,diffusion barriers,high-temperatureresistors,and hard and corrosion-resistant electrical contacts.The deposition tech-nique most found in literature,is probably Chemical Vapour Deposition (CVD).Dif-ferent gasses in a certain ratio are combined,and through the chemical reaction ofthese gasses,a thin ﬁlm is deposited.As an example,Lundberg et al.[7] depositedWCﬁlms from aWF6/C3H8/H2(1:15:16) mixture.CVD is a relatively slow pro-cess,so other techniques are preferred for their more production-friendly depositionspeed.Co-evaporation is the evaporation of the transition metal and of the carbon41Part II.Thin ﬁlmsolid-state reactions forming Carbidesfrom another source,at the same time.Similar to this is co-sputtering,where thematerials are sputtered from different (one-element) targets,at the same time.In re-active sputtering,one adds a ’reactive’ gas to the sputtering plasma (so extra to the Argas,used for sputtering).For carbide formation,methaneCH4is the obvious choicefor the reactive gas.Further,sputtering fromsintered compound-targets and,last butnot least,sputtering of layered thin ﬁlms are also used.The latter technique is usedin this work.Each deposition technique has its own essential parameters (like heattreatments,gas pressure,substrate temperature,...).The goal of this work is to be a guide for the production of carbide thin ﬁlmsstarting from sputtered (one-element) thin ﬁlms,followed by a solid-state reaction.This kind of reaction is very important in the industry of micro-electronics.In silicon-based technology (i.e.the largest part of the micro-electronics industry),metal-silicon